Abstract:
We study planar homeomorphisms $f: \Omega\subset R^2 $ onto $\to \Omega' \subset R^2$, $f=(u,v)$, which are absolutely continuous on lines parallel to the axes (ACL) together with their inverse $f^{-1}$. The main result is that $u$ and $v$ have almost everywhere the same critical points. This generalizes a previous result ([6]) concerning bisobolev mappings. Moreover we construct an example of a planar ACL-homeomorphism not belonging to the Sobolev class $W_{l o c}^{1,1}$.